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Sharp Li--Yau Inequalities for Dunkl Harmonic Oscillators
Huaiqian Li, Bin Qian · 2023-03-21 · via math.PR updates on arXiv.org

We study the Li--Yau inequality for the heat equation corresponding to the Dunkl harmonic oscillator, which is a non-local Schrödinger operator parameterized by reflections and multiplicity functions. In the particular case when the reflection group is isomorphic to $\mathbb{Z}_2^d$, the result is sharp in the sense that equality is achieved by the heat kernel of the classic harmonic oscillator. We also provide the application on parabolic Harnack inequalities.

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